Movement on a sphere (elliptic integrals)

[springo]

Homework Statement

A point moves with constant speed (value) over a sphere, following the curve defined by: f = t = l
For t=0, the point is at (t,f) = (0,0) and for t=3 it's at (pi/4, pi/4).
How long does it take to reach the north pole of the sphere?

Homework Equations

The parametric equations for this sphere are:
x = 5·cos f·cos t
y = 5·cos f·sin t
z = 5·sin f

The Attempt at a Solution

OK first of all, the parametric equations turn into:
x = 5·cos² l
y = 5·cos l·sin l
z = 5·sin l

Then we know that:
v² = x'² + y'² + z'²
So we find:
x' = -5·sin(2l)
y' = 5·cos(2l)
z' = 5·cos l

By adding them up, we simplify the squared sines-cosines:
v² = 25(1 + ·cos² l)·(dl/dt)²
v·dt = 5√(1 + ·cos² l)·dl

However I don't know how to find v, and I'm not sure this is correct so far.

Thank you for your help

 

[springo]

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